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Kenji and Ed are each assigned a paper for a class they share. Kenji decides to write $7$ pages at a time while Ed decides to write $3$ pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had? $\newline$ $\_\_\_\_\_$ pages

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GCF and LCM: word problems

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Q. Kenji and Ed are each assigned a paper for a class they share. Kenji decides to write

7

pages at a time while Ed decides to write

3

pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had?

\newline

\_\_\_\_\_

pages

Identify Concept: Identify the mathematical concept needed to solve the problem. Since Kenji and Ed need to write the same number of pages, and they write in different set amounts per session, we need to find the Least Common Multiple (LCM) of $7$ and $3$ .
Calculate LCM: Calculate the LCM of $7$ and $3$ . Since $7$ and $3$ are both prime numbers, their LCM is simply their product: $7 \times 3 = 21$ .
Verify Solution: Verify the solution by checking if $21$ is divisible by both $7$ and $3$ . $21 \div 7 = 3$ , and $21 \div 3 = 7$ , both of which are integers, confirming that $21$ is indeed the LCM.

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